Lattice width directions and Minkowski's 3^d-theorem

J. Draisma, T.B. McAllister, B. Nill

Research output: Book/ReportReportAcademic


We show that the number of lattice directions in which a d- dimensional convex body in Rd has minimum width is at most 3d -1, with equality only for the regular cross-polytope. This is deduced from a sharpened version of the 3d-theorem due to Hermann Minkowski (22 June 1864-12 January 1909), for which we provide two independent proofs.
Original languageEnglish
Number of pages10
Publication statusPublished - 2009

Publication series [math.CO]


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